How reliable are pseudocontact shifts induced in proteins and ligands by mobile paramagnetic metal tags? A modelling study

The anisotropic component of the magnetic susceptibility tensor (Delta chi tensor) associated with various paramagnetic metal ions can induce pseudocontact shifts (PCSs) and residual dipolar couplings (RDCs) in proteins, yielding valuable restraints in structural studies. In particular, PCSs have successfully been used to study ligands that bind to proteins tagged with a paramagnetic metal ion, which is of great interest in fragment-based drug design. To create easy-to-interpret PCSs, the metal ion must be attached to the protein in a rigid manner. Most of the existing methods for site-specific attachment of a metal tag, however, result in tethers with residual flexibility. Here we present model calculations to quantify the extent, to which mobility of the metal-binding tag can compromise the quality of the Delta chi tensor that can be determined from the PCSs observed in the protein. Assuming that the protein can be approximated by a sphere and the tag is attached by a single tether, the results show that a single effective a dagger chi tensor can describe the PCSs and RDCs of the protein spins very well even in the presence of substantial tag mobility, implying that PCSs of ligands in binding pockets of the protein can be predicted with similar accuracy. In contrast, the quality of the PCS prediction for nuclear spins positioned above the surface of the protein is significantly poorer, with implications for studies of protein-protein complexes. The simulations probed the sensitivity of the effective Delta chi tensor to different parameters, including length of the tether between protein and metal ion, protein size, type and amplitude of tag motion, tensor orientation relative to the protein and direction of tag motion. Tether length and amplitude of motion were identified as two key parameters. It is shown that the amplitude of tag motions cannot be quantified by simple comparisons of the effective Delta chi tensor with the alignment tensor determined from RDCs.